A Geometrical Approach to Maximum Likelihood Estimation for Infinite-Dimensional Gaussian Location. I

Abstract

Previous article Next article A Geometrical Approach to Maximum Likelihood Estimation for Infinite-Dimensional Gaussian Location. IB. S. Tsirel’sonB. S. Tsirel’sonhttps://doi.org/10.1137/1127049PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] I. A. Ibragimov and , R. Z. Khas'minskii, On the estimation of an infinite-dimensional parameter in Gaussian white noise, Soviet Math. Doklady, 18 (1977), 1307–1309 0389.62023 Google Scholar[2] I. A. Ibragimov and , R. Z. Khas'minskii, A problem of statistical estimation in Gaussian white noise, Soviet Math. Doklady, 18 (1977), 1351–1354 0389.62024 Google Scholar[3] V. N. Sudakov, Geometric problems in the theory of infinite-dimensional probability distributions, Proc. Steklov Inst. Math., (1979), i–v, 1–178 80e:60052 0409.60005 Google Scholar[4] B. S. Tsirel'son, A natural modification of a random process, and its applications to series of random functions and to Gaussian measures, Zap. Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), 55 (1976), 35–63, 199–200, (In Russian.) 53:11727 0408.60033 Google Scholar[5] B. L. Rao, Estkmation of a unimodal density, Sankhyā Ser. A, 31 (1969), 23–36 42:2579 Google Scholar[6] I. A. Ibragimov and , R. Z. Khas'minskii, Asymptotic behavior of statistical estimators of the location parameter for samples with continuous density with.singularities, Zap. Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), 41 (1974), 67–93, 166–167, (In Russian.) 51:2108 0391.62015 Google Scholar[7] M. S. Ermakov, On sufficient statistics for families of densities with "moving carrier", Theory Prob. Appl., 21 (1976), 657–661 0362.62003 Google Scholar[8] Yu. A. Davydov, On the absolute continuity of the distributions of functionals of random processes, Theory Prob. Appl., 23 (1978), 218–219 LinkGoogle Scholar[9] B. S. Tsirel'son, , I. A. Ibragimov and , V. N. Sudakov, Norms of Gaussian sample functions, Lectures Notes in Mathematics, Vol. 550, Springer, Berlin, 1976, 20–41 0359.60019 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Invariance-based approach: general methods and pavement engineering case study28 July 2021 | International Journal of General Systems, Vol. 50, No. 6 Cross Ref Limit Theorems as Blessing of Dimensionality: Neural-Oriented Overview22 April 2021 | Entropy, Vol. 23, No. 5 Cross Ref Scale-Invariance Ideas Explain the Empirical Soil-Water Characteristic Curve Cross Ref On an Exponential Functional for Gaussian Processes and Its Geometric Foundations23 March 2019 | Journal of Mathematical Sciences, Vol. 238, No. 4 Cross Ref Dow Theory’s Peak-and-Trough Analysis Justified9 September 2017 Cross Ref Sieves, Method of29 September 2014 Cross Ref On the Gaussian representation of intrinsic volumesStatistics & Probability Letters, Vol. 78, No. 10 Cross Ref Sieves, Method of15 August 2006 Cross Ref Intrinsic volumes and Gaussian processes1 July 2016 | Advances in Applied Probability, Vol. 33, No. 2 Cross Ref Some Estimation Problems in Infinite Dimensional Gaussian White Noise Cross Ref Gaussian measures on linear spacesJournal of Mathematical Sciences, Vol. 79, No. 2 Cross Ref Stochastic extremal problems and the strong Markov property of random fields16 October 2007 | Russian Mathematical Surveys, Vol. 43, No. 2 Cross Ref A Geometric Approach to Maximum Likelihood Estimation for Infinite-Dimensional Location. IIIB. S. Tsirel’son28 July 2006 | Theory of Probability & Its Applications, Vol. 31, No. 3AbstractPDF (910 KB)On the Distribution of the Maximum of a Gaussian ProcessM. A. Lifshits1 August 2006 | Theory of Probability & Its Applications, Vol. 31, No. 1AbstractPDF (872 KB)A Geometric Approach to Maximum Likelihood Estimation for Infinite- Dimensional Gaussian Location. IIB. S. Tsirel’son28 July 2006 | Theory of Probability & Its Applications, Vol. 30, No. 4AbstractPDF (957 KB) Volume 27, Issue 2| 1983Theory of Probability & Its Applications History Submitted:05 December 1978Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1127049Article page range:pp. 411-418ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics